Topological derivatives for layout generation of crash-loaded structures

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The layout (topology and shape) of mechanical components has a very large influence on their functionality and quality. In the linear static, effective algorithms for the generation of good layouts exist. On the one hand, there are methods, which subdivide the design domain in many small parts (often over 10 Mio. Voxel) and decide for every part, is there material required or not. Based on this layout proposal, a component structure is derived in a post processing procedure. On the other hand, there are methods, which describe the component structure and the topology changes directly in CAD. Here, no post-processing activities are necessary. The extension of these topology optimization methods for non-linear tasks is a big challenge. Especially, the generation of layouts for crash-loaded structures needs extensive researches. It is necessary to consider non-linear material models, large displacements and deformations as well as contact phenomena. This DFG research project deals with the possible extensions of the method of topological derivatives, which is powerful for the layout generations in linear static applications. The objective is to determine the possibility to predict the effects which result from the removal of structural domains resp. the integration of cut-outs in crash-loaded structures. The scientific issues are the following: 1) Is it possible to extend the method of topological derivatives for crash-absorbing structures? 2) Which non-linear phenomena can be considered? 3) How can the new method execute a self-contained layout generation?The research project is subdivided in 7 work packages. The first three work packages generate the development frame, in order to integrate the following work packages. Algorithms, based on the topology derivatives, will developed for layout generations. It is about the use of the topological derivatives as an indicator for sensitive positions in the component during the crash structure development and the extension of the voxel method and the bubble method. These first work packages attend the research project over the whole period. The following work packages deal with the crash relevant behaviors like material non-linearity (plasticity and strain rate dependency), buckling phenomena, time dependency and contact (self contact and contact to neighbor components). Each work package starts with a functional analysis. The superficial focus is on the development of completely analytical description for the topological derivatives. If this is not possible, research is carried out on suitable concepts for a numerical solutions. The idea is the generation of meta-models based on a design-of-experiment driven crash simulations.